An extended Freudenthal magic square in characteristic 3

DOI10.1016/j.jalgebra.2007.07.028zbMath1172.17010arXivmath/0605379OpenAlexW2569559653MaRDI QIDQ2466931

Alberto Elduque, Isabel Cunha

Publication date: 16 January 2008

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0605379

zbMATH Keywords

trialityTits constructioncontragredient Lie superalgebracharacteristic threeexceptional simple Lie algebraFreudenthal magic squarecentral simple Jordan algebra of degree threeexceptional classical Lie superalgebraextended Freudenthal magic squareunital composition algebra

Mathematics Subject Classification ID

Color Lie (super)algebras (17B75) Exceptional (super)algebras (17B25) Simple, semisimple, reductive (super)algebras (17B20) Lie (super)algebras associated with other structures (associative, Jordan, etc.) (17B60) Modular Lie (super)algebras (17B50)

Related Items (7)

The extended Freudenthal magic square and Jordan algebras ⋮ Representations of alternative algebras and superalgebras ⋮ From octonions to composition superalgebras via tensor categories ⋮ Deformations of the Lie algebra \(\mathfrak{o}(5)\) in characteristics \(3\) and \(2\) ⋮ On finite dimensional Nichols algebras of diagonal type ⋮ Affine connections on 3-Sasakian homogeneous manifolds ⋮ New simple modular Lie superalgebras as generalized prolongs

Cites Work

• Some new simple modular Lie superalgebras
• The magic square and symmetric compositions. II
• Nonassociative coefficient algebras for Steinberg unitary Lie algebras
• Magic squares and matrix models of Lie algebras.
• Triality, exceptional Lie algebras and Deligne dimension formulas.
• The magic square and symmetric compositions
• Lie algebras graded by finite root systems and intersection matrix algebras
• New simple Lie superalgebras in characteristic 3
• The extended Freudenthal magic square and Jordan algebras
• Lie groups in the foundations of geometry
• The Tits Construction and the Exceptional Simple Classical Lie Superalgebras
• The octonions
• COMPOSITION SUPERALGEBRAS
• Introduction to Lie Algebras and Representation Theory
• Lie superalgebras
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